As \((A,\delta ,\rho )\)  is a \((K,H)\) -bicomodule algebra, it follows that (REF ) is a short exact sequence of \((K,H)\) -bicomodule left \(A\) -modules. Applying the 2-cocycle
deformation functor from [1]} or
[2]}, we obtain
the short exact sequence of \((K,H)\) -bicomodule left \(A_\theta \) -modules
\({0[r]&\Omega ^1_\mathrm {hor}(A)_\theta [r]& \Omega ^1(A)_\theta [r]^-{\overline{\mathrm {ver}}}& \big ( A\otimes \mathfrak {h}^\vee \big )_\theta [r] & 0.}\) 
